At the time of the Justinian Plague (~541 AD), did people know how the plague spread, i.e. that rats and fleas were the vectors? What measures were taken to protect against infection and to treat the infected?

Allmost certainly not. For most of recorded history (right up to the Victorian age), most cultures had no idea about 'gem theory' - see the work of Robert Koch. Most cultures tended to put the spread of 'plauges' to bad smells - literally 'malaria' (from where that particular disease gets its name). In fact, the curse of the modern office environment - air conditioning - was invented to try to stop the spread of diseases carried on bad smells.

Without the concept of germ theory, the importance of vectors to spread diseases from one species to another would, probably, not have been thoought about. After all, most people would have carried a variety of parasites most of the time - both internally and externally. So a few more flea bits, for most people, may not have actually been noticed.

I believe that there were a number of plague outbreaks in what became England post AD 400, pre 700, which may have contributed to the decline of town life; has anyone come across any information on this?